Talk:Hahn-Banach theorem
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if V is a normed vector space with subspace U (not necessarily closed) and if z is an element of V not in the closure of U, then there exists a continuous linear map ψ : V -> K with ψ(x) = 0 for all x in U, ψ(z) = 1, and ||ψ|| = ||z||-1.
I think "not necessarily closed" is wrong here. But can't make up a counterexample right now.
- What do you mean "wrong" ? It's a hypothesis, it cannot be right or wrong... It could be unnecessary to mention it, but it can't be wrong.